- 97-309 Govin M., Chandre C., Jauslin H.R.
- KAM-Renormalization Group Analysis of Stability in Hamiltonian Flows
Jun 3, 97
(auto. generated ps),
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Abstract. We study the stability and break-up of invariant tori in Hamiltonian flows
using a combination of KAM theory and renormalization group techniques.
We implement the scheme numerically for a family of
Hamiltonians quadratic in the actions to analyse the strong coupling
We show that the KAM iteration converges up to the critical coupling
at which the torus breaks up. Adding a renormalization scheme consisting of
a rescaling of phase space and a shift of
the relevant resonances, we obtain a much more efficient method that
allows to determine the critical coupling with high accuracy.
The results indicate that this
approach captures the essential physical mechanism of the
break-up of invariant tori. We determine a non-trivial fixed point of the
renormalization transformation, and discuss the associated universality